Hi Snobuny,
Welcome to our Pain Management Forum. You've asked a good question and although it may seem straight forward there's a lot to be considered.
Oxymorphone is seven times stronger then morphine while hydromorphone is five times stronger than morphine. They are in the same synthetic family of drugs. Although on "paper" Oxymorphone is more potent then Hydromorphone that doesn't necessarily mean that one is more effective then the other. Pain management is individualized. What's most effective for me may not be for you and vise versa.
Some ppl swear that oxycodone is more effective then hydrocodone... that isn't true for me and my chronic pain. However if I have surgical pain then it is true. So not only do you have to take into account a person's individual reaction you must also consider the site or source of pain.
I hope this was helpful. It may be more information then you were seeking. Unfortunately in my opinion there really is no real cut and dried answer. I hope you'll keep in touch and be active in our community.
Peace,
~Tuck